70 LIMITS AND FLUXIONS 



ing Quantities, he [Newton] elsewhere calls by the 

 name of Moments, . . : By Moments we may 

 understand the nascent or evanescent Elements or 

 Principles of finite Magnitudes, but not Particles 

 of any determinate Size, or Increments actually 

 generated ; for ali such are Quantities, themselves 

 generated of Moments." 



92. "The magnitudes of the momentaneous 

 Increments or Decrements of Quantities are not 

 regarded in the Method of Fluxions, but their first 

 or last Proportions only ; that is, the Proportions 

 with which they begin or cease to exist." . . . 

 "The ultimate Ratios with which synchronal 

 Increments of Quantities vanish, are not the Ratios 

 of finite Increments, but Limits which the Ratios 

 of the Increments attain, by having their magni- 

 tudes infinitely diminish'd. . . . There are certain 

 determinate Limits to which ali such Proportions 

 perpetually tend, and approach nearer than by any 

 assignable Difference, but never attain before the 

 Quantities themselves are infinitely diminish'd ; 

 or 'till the Instant they evanesce and become 

 nothing." "The Pluxions of Quantities are very 

 nearly as the Increments of their Fluents generated 

 in the least equal Particles of Time," and they 

 "are accurately in the first or last Proportions of 

 their nascent or evanescent Increments." "The 

 Fluxions of Quantities are only velocities. ..." 

 Again, ". . . to obtain the Ratios of Fluxions, 

 the corresponding synchronal or isochronal Incre- 

 ments must be lessened in infiniiuni. For the 



